Speaker: Richard Samuels, Department of Philosophy, The Ohio State University

Subject: "How to Acquire Number Concepts: A New Puzzle (With Stewart Shapiro and Eric Snyder)"

Refreshments served at 3:15 p.m.

Philosophers and psychologists have long been interested in how human beings learn mathematical concepts in general, and natural number concepts, in particular. Efforts to explain how such concepts are learned, however, have resulted in a number of puzzles and problems, which have led some to conclude that these concepts cannot be learned. In this talk, we first sketch some of the more important of these puzzles, and then articulate a new one that rests upon an apparent tension between two of the best empirical probes into our natural number concepts – linguistic semantics and developmental psychology. On the face of it, the dominant views in these respective fields are in tension with each other, so that if the semanticists are right, then our best accounts of how natural number concepts are learned must be wrong. Having set out this puzzle in some detail, we argue that a structuralist conception of the naturals offers a partial resolution of this apparent tension.